Answer
$f(x)=-4$
Work Step by Step
Rewrite as shown below.
$f(3)=-4$ as $(3,-4)$
and $f(5)=-4$ as $(5,-4)$
Let $(x_1,y_1)=(3,-4)$ and $(x_2,y_2)=(5,-4)$.
Slope
$\Rightarrow m =\frac{y_2-y_1}{x_2-x_1}$
Substitute all the values.
$\Rightarrow m =\frac{-4-(-4)}{5-3}$
Simplify.
$\Rightarrow m =\frac{-4+4}{2}$
$\Rightarrow m =\frac{0}{2}$
$\Rightarrow m =0$
The point-slope form.
$\Rightarrow y-y_1=m(x-x_1)$
Substitute all the values.
$\Rightarrow y-(-4)=0(x-3)$
Simplify.
$\Rightarrow y+4=0$
Subtract $4$ from each side.
$\Rightarrow y+4-4=0-4$
Simplify.
$\Rightarrow y=-4$
Hence, the function is $f(x)=-4$.
